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Bob has 20 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (10 – x) feet wide. What value of x will give the largest area, in square feet, for the garden?

Verified Answer :

For the problem presented with the specific given values, the value of x
that will give the largest
area in square feet for the garden is 5. I am hoping that this answer
has satisfied your query about this specific question.

Answer:

Step-by-step explanation:

Alright, lets get started.

The length of the rectangular garden is x

The width of the rectangular garden is (10-x)

So the area will be = \(length * width\)

So the area will be = \(x*(10-x)= 10x-x^2\)

For this area to be maximum, the derivative of this area must be equal to zero.

\(\frac{d}{dx}(10x-x^2) = 0\)

\(10-2x = 0\)

\(2x=10\)

\(x=5\)

Hence the value of x will be for largest area.   :   Answer

Hope it will help :)

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